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How to Plot a Lognormal Curve

By Suman Medda; Updated April 24, 2017

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The lognormal distribution is used in probability for normally distributing the logarithm of a random variable. Variables that can be written as the product of multiple independent random variables can also be distributed in this way. When plotting a lognormal distribution, there are a couple of important aspects that you should not miss; there is a formula that will be useful during this process. Plot by hand on paper or electronically using specialized software.

Sort the point values of the random variable to be lognormally distributed from the smallest to the largest.

Check to see if all of the values are positive. If they are not, the lognormal distribution plotting cannot be done.

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Compute the natural logarithm for each of the values in the previous step. This is a vital step, since the definition of lognormal curves involves plotting the logarithmic function of random variables.

Compute the empirical cumulative probability of each value using the formula p(n) = (n – 0.5) / N. "N" is the total number of elements, while "n" is used to denote the current point value.

Compute the inverse error function for each element. The inverse error function is defined as erf(x) = 2 / sqrt(π) * integral of e^x^2 dt. In this case, "x" will be replaced with 2p-1, for each one of the "p" values computed above.

Plot the points with the coordinates (z(pn), ln(xn)), where xn is used to denote the point values from the first step and z(pn) is the output from Step 5.

Draw a line to connect the points. This is the final lognormal curve for this distribution.

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About the Author

Suman Medda holds a B.S. in biomedical engineering with a specialty in tissue engineering. His biomedical research abstracts have been featured in the Southeastern Surgical Conference. He enjoys technical and scientific writing and has been writing since 2007.